DescriptionInverse transformation method for exponential distribution.jpg

English: Random numbers y_i are generated from a uniform distribution between 0 and 1, i.e. Y ~ U(0, 1). They are sketched as colored points on the y-axis. Each of the points is mapped according to x=F^-1(y), which is shown with gray arrows for two example points.
In this example, we have an exponential distribution. Hence, for x ≥ 0, the probability density is rho(x) = c*exp(-c*x) and the cumulated probability function is F(x) = 1 - exp(c*x). Therefore, F^-1(y) = - ln(1-y) / c. We can see that using this method, many points end up close to 0 and only very few points are mapped to high x-values - just as it is expected for an exponential distribution.

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